To copy, rename or delete a project you first have to select the project you wish to alter. Once a project is selected the 3 other buttons in the top right of the navigation bar will no longer be grayed out. 

After selecting a project click on the copy button in the top right. This will copy all jobs, database connection settings, mappings, and schedules. The only setting that is (intentionally) not copied over is the Next Job for Job Chaining.

After selecting a project click on the delete (the circled X) button in the top right. A final warning will popup asking "Do you really want to delete this project and all jobs contained within it?"